Question

ratioof period of revolution of two planets around a massive star is 32 : 1 find the ratio of their distance from the centre of the star

Answer 1

By Kepler's  law

           $\frac{t_{1} ^{2} }{t_{2} ^{2} } = \frac{r_{1} ^{3} }{r_{2} ^{3} }$

         ⇒ $\frac{32^{2} }{1^{2} } = \frac{r_{1} ^{3} }{r_{2} ^{3} }$

         ⇒$\frac{1024}{1} =\frac{r_{1} ^{3} }{r_{2} ^{3} }$

         ⇒ $\frac{\sqrt[3]{1024} }{\sqrt[3]{1} } = \frac{r_{1} }{r_{2} }$

  Hence this is the answer.